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W. Heisenberg, Der Teil und das Ganze (Piper, München, 1969); English translation: Physics and beyond; encounters and conversations (Harper & Row, New York, 1971)
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W. Heisenberg, Der Teil und das Ganze (Piper, München, 1969); English translation: Physics and beyond; encounters and conversations (Harper & Row, New York, 1971).
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Πλ&α´τωνοςΠολιτε&ιacute;α; English translation: Plato, Republic, Book VII, p. 514, in The Loeb Classical Library L276, Vol. VI (Harvard University Press, Cambridge, MA, 1935)
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Πλ&α´τωνοςΠολιτε&ιacute;α; English translation: Plato, Republic, Book VII, p. 514, in The Loeb Classical Library L276, Vol. VI (Harvard University Press, Cambridge, MA, 1935).
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S. de Groot, La Transformation de Weyl et la Fonction de Wigner: Une Forme Alternative de la Méchanique Quantique (Les Presses de l'Université de Montréal, Montréal, 1974)
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See also J. E. Moyal, Proc. Cambridge Philos. Soc. 45, 99 (1949); S. de Groot, La Transformation de Weyl et la Fonction de Wigner: Une Forme Alternative de la Méchanique Quantique (Les Presses de l'Université de Montréal, Montréal, 1974).
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M. Hillery, R. F. O'Connell, M. O. Scully and E. P. Wigner, Phys. Rep. 106, 121 (1984).
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D. T. Smithey, M. Beck, M. G. Raymer and A. Faridani, Phys. Rev. Lett. 70, 1244 (1993).
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D. T. Smithey, M. Beck, J. Cooper and M. G. Raymer, Phys. Scr. T48, 35, (1993)
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D. T. Smithey, M. Beck, J. Cooper and M. G. Raymer, Phys. Rev. A 48, 3159 (1993)
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Phys. Rev. A
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M. Beck, D. T. Smithey, J. Cooper and M. G. Raymer, Opt. Lett. 18, 1259 (1993).
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Opt. Lett.
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19
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85037222780
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(Springer, Berlin, 1980) raised the question whether the wave function can be reconstructed from position and momentum distributions. The general problem of state reconstruction was stated by
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A look at the history of the quantum-state measurement schemes may be interesting. W. Pauli, General Principles of Quantum Mechanics (Springer, Berlin, 1980) raised the question whether the wave function can be reconstructed from position and momentum distributions. The general problem of state reconstruction was stated by U. Fano, Rev. Mod. Phys. 29, 74 (1957).
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Pauli, W.1
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Invented a recipe to measure the spin density matrix. Later, W. Band and J. L. Park, Found. Phys. 1, 133 (1970); 1, 211 (1971); 1, 339 (1971)
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R. G. Newton and B.-L. Young, Ann. Phys. (N.Y.) 49, 393 (1968) invented a recipe to measure the spin density matrix. Later, W. Band and J. L. Park, Found. Phys. 1, 133 (1970); 1, 211 (1971); 1, 339 (1971).
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Young, L.2
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0007884470
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Am. J. Phys. 47, 188 (1979) developed a general procedure for solving the state-inference problem and gave explicit examples for spin, spin 1, and one-dimensional spinless systems. I. D. Ivanović, J. Math. Phys. 24, 1199 (1983) refined this method. Another paper by Ivanović 35 served as the mathematical basis for Wootters' work on the subject.
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Ivanovi, I.D.1
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Found. Phys. 19, 3 (1989)
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A. Royer, Phys. Rev. Lett. 55, 2745 (1985); Found. Phys. 19, 3 (1989)
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A scheme to measure the vibrational state of trapped ions was proposed by S. Wallentowitz and W. Vogel, Phys. Rev. Lett. 75, 2932 (1995).
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The special case of pure states was considered in J. Bohn, Phys. Rev. Lett. 66, 1447 (1991).
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Fundamental limits upon the measurements of state vectors were considered by K. R. W. Jones, Phys. Rev. A 50, 3682 (1994).
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Th. Richter, Phys. Lett. A 211, 327 (1996);U. Leonhardt, M. Munroe, T. Kiss, and M. G. Raymer, Th. Richter, Opt. Commun. (to be published). Note that even the state of anharmonic wave packets can be inferred.
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Phys. Lett. A
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Th. Richter and A. Wünsche, Phys. Rev. A (to be published)
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see U. Leonhardt and M. G. Raymer, Phys. Rev. Lett. 76, 1985 (1996); Th. Richter and A. Wünsche, Phys. Rev. A (to be published).
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K. R. Popper, Quantum theory and the schism in physics (Hutchinson, London, 1982), pp. 125–130
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K. R. Popper, Quantum theory and the schism in physics (Hutchinson, London, 1982), pp. 125–130.
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Continuous Wigner functions for spin systems are considered in G. S. Agarwal, Phys. Rev. A 24, 2889 (1981).
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Strictly speaking, the presented formalism is only valid for odd-dimensional systems. However, it can be easily extended to even-dimensional ones using the theory developed here and in Ref. 11
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T. Opatrný, V. Buzek, J. Bajer and G. Drobný, Phys. Rev. A 52, 2419 (1995). Strictly speaking, the presented formalism is only valid for odd-dimensional systems. However, it can be easily extended to even-dimensional ones using the theory developed here and in Ref. 11.
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W. P. Schleich, R. J. Horowicz, and S. Varro, in Quantum Optics V, edited by J. D. Harvey and D. F. Walls (Springer, Berlin, 1989).
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See also D. Galetti and A. F. R. De Toledo Piza, Physica A 149, 267 (1988).
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I. Sh. Averbukh and N. F. Perel'man, Usp. Fiz. Nauk. 161, 41 (1991) [Sov. Phys. Usp. 34, 572 (1991)];M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, Phys. Rev. Lett. (submitted).
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Quantum control schemes can be used to create arbitrary states of Zeeman multiplets. This is a necessary ingredient in the quantum-state synthesis via adiabatic passage by A. S. Parkins, P. Marte, P. Zoller and H. J. Kimble, Phys. Rev. Lett. 71, 3095 (1993).
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A. S. Parkins, P. Marte, P. Zoller, O. Carnal and H. J. Kimble, Phys. Rev. A 51, 1578 (1995).
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106
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85037186428
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J. F. Clauser and J. P. Dowling (unpublished) for an analogue in classical optics. A d-period diffraction grating represents the spin system and the classical propagation of light plays the role of the precession
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J. F. Clauser and J. P. Dowling (unpublished) for an analogue in classical optics. A d-period diffraction grating represents the spin system and the classical propagation of light plays the role of the precession.
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109
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85037252404
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N. M. Korobov, Trigonometricheskie summy i ikh prilozhenia (Nauka, Moscow, 1989), Sec. 3. Sums of the type (88) are called Gauss sums. See also Ref. 33
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N. M. Korobov, Trigonometricheskie summy i ikh prilozhenia (Nauka, Moscow, 1989), Sec. 3. Sums of the type (88) are called Gauss sums. See also Ref. 33.
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110
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34748841353
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references cited therein
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A. Barenco, Ch. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin and H. Weinfurter, Phys. Rev. A 52, 3457 (1995), and references cited therein.
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Shor, P.6
Sleator, T.7
Smolin, J.A.8
Weinfurter, H.9
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